Recall the Jacobi-Anger expansion [1]}
\(e^{-ik\hat{x}\cdot y} = 2\pi \sum _{m=-\infty }^{\infty }(-i)^{m}\mathfrak {B}_{m}(kr)\phi _{m}(\theta _{\hat{x}})\phi _{-m}(\theta _y),\quad y\in {\mathbb {R}}^2.\) 
